Bit interleaver for low-density parity check codeword having length of 64800 and code rate of 2/15 and 1024-symbol mapping, and bit interleaving method using same

ABSTRACT

A bit interleaver, a bit-interleaved coded modulation (BICM) device and a bit interleaving method are disclosed herein. The bit interleaver includes a first memory, a processor, and a second memory. The first memory stores a low-density parity check (LDPC) codeword having a length of 64800 and a code rate of 2/15. The processor generates an interleaved codeword by interleaving the LDPC codeword on a bit group basis. The size of the bit group corresponds to a parallel factor of the LDPC codeword. The second memory provides the interleaved codeword to a modulator for 1024-symbol mapping.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/664,707, filed Mar. 20, 2015, which claims the benefit of KoreanPatent Application No. 10-2015-0023411, filed Feb. 16, 2015, which ishereby incorporated by reference herein in its entirety.

BACKGROUND 1. Technical Field

The present disclosure relates generally to an interleaver and, moreparticularly, to a bit interleaver that is capable of distributing bursterrors occurring in a digital broadcast channel.

2. Description of the Related Art

Bit-Interleaved Coded Modulation (BICM) is bandwidth-efficienttransmission technology, and is implemented in such a manner that anerror-correction coder, a bit-by-bit interleaver and a high-ordermodulator are combined with one another.

BICM can provide excellent performance using a simple structure becauseit uses a low-density parity check (LDPC) coder or a Turbo coder as theerror-correction coder. Furthermore, BICM can provide high-levelflexibility because it can select modulation order and the length andcode rate of an error correction code in various forms. Due to theseadvantages, BICM has been used in broadcasting standards, such as DVB-T2and DVB-NGH, and has a strong possibility of being used in othernext-generation broadcasting systems.

However, in spite of those advantages, BICM suffers from the rapiddegradation of performance unless burst errors occurring in a channelare appropriately distributed via the bit-by-bit interleaver.Accordingly, the bit-by-bit interleaver used in BICM should be designedto be optimized for the modulation order or the length and code rate ofthe error correction code.

SUMMARY

At least one embodiment of the present invention is directed to theprovision of an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

At least one embodiment of the present invention is directed to theprovision of a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 2/15 and a modulatorperforming 1024-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

In accordance with an aspect of the present invention, there is provideda bit interleaver, including a first memory configured to store alow-density parity check (LDPC) codeword having a length of 64800 and acode rate of 2/15; a processor configured to generate an interleavedcodeword by interleaving the LDPC codeword on a bit group basis, thesize of the bit group corresponding to a parallel factor of the LDPCcodeword; and a second memory configured to provide the interleavedcodeword to a modulator for 1024-symbol mapping.

The 1024-symbol mapping may be NUC (Non-Uniform Constellation) symbolmapping corresponding to 1024 constellations (symbols).

The parallel factor may be 360, and each of the bit groups may include360 bits.

The LDPC codeword may be represented by (u_(0,)u₁, . . . , u_(N) _(ldpc)⁻¹) (where N_(ldpc) is 64800), and may be divided into 180 bit groupseach including 360 bits, as in the following equation:

X _(j) ={u _(k)|360×j≤k<360×(j+1), 0≤k<N _(ldpc)} for 0≤j<N _(group)

where X_(j) is an j-th bit group, N_(ldpc) is 64800, and N_(group) is180.

The interleaving may be performed using the following equation usingpermutation order:

Y _(j) =X _(π(j)) 0≤j≤N _(group)

where X_(j) is the j-th bit group, Y_(j) is an interleaved j-th bitgroup, and π(j) is a permutation order for bit group-based interleaving(bit group-unit interleaving).

The permutation order may correspond to an interleaving sequencerepresented by the following equation:

interleaving sequence={157 25 107 160 37 138 111 35 29 44 15 162 66 2049 126 89 147 159 174 142 26 146 10 164 152 57 110 83 167 169 16 6 17262 173 7 145 4 67 115 50 39 72 79 74 40 132 42 30 163 161 55 143 63 11786 121 2 28 69 150 24 177 43 158 27 21 128 46 118 114 127 135 92 76 1994 179 3 52 101 137 84 73 108 91 120 47 1 102 58 68 82 59 119 64 31 61105 103 151 124 70 8 155 90 166 41 45 178 113 140 75 148 109 100 125 11116 34 36 176 170 156 136 171 122 78 87 106 123 149 17 99 175 18 9 165153 12 81 77 60 93 104 13 5 88 96 141 133 154 144 48 97 23 14 98 53 134112 65 0 130 32 168 33 131 22 38 56 80 95 71 85 139 129 51 54}

In accordance with another aspect of the present invention, there isprovided a bit interleaving method, including storing an LDPC codewordhaving a length of 64800 and a code rate of 2/15; generating aninterleaved codeword by interleaving the LDPC codeword on a bit groupbasis corresponding to the parallel factor of the LDPC codeword; andoutputting the interleaved codeword to a modulator for 1024-symbolmapping.

In accordance with still another aspect of the present invention, thereis provided a BICM device, including an error-correction coderconfigured to output an LDPC codeword having a length of 64800 and acode rate of 2/15; a bit interleaver configured to interleave the LDPCcodeword on a bit group basis corresponding to the parallel factor ofthe LDPC codeword and output the interleaved codeword; and a modulatorconfigured to perform 1024-symbol mapping on the interleaved codeword.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more clearly understood from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention;

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention;

FIG. 3 is a diagram illustrating the structure of a parity check matrix(PCM) corresponding to an LDPC code to according to an embodiment of thepresent invention;

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800;

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200;

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence;

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention; and

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings. Repeated descriptions anddescriptions of well-known functions and configurations that have beendeemed to make the gist of the present invention unnecessarily obscurewill be omitted below. The embodiments of the present invention areintended to fully describe the present invention to persons havingordinary knowledge in the art to which the present invention pertains.Accordingly, the shapes, sizes, etc. of components in the drawings maybe exaggerated to make the description obvious.

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention.

Referring to FIG. 1, it can be seen that a BICM device 10 and a BICMreception device 30 communicate with each other over a wireless channel20.

The BICM device 10 generates an n-bit codeword by encoding k informationbits 11 using an error-correction coder 13. In this case, theerror-correction coder 13 may be an LDPC coder or a Turbo coder.

The codeword is interleaved by a bit interleaver 14, and thus theinterleaved codeword is generated.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group). In this case, the error-correction coder 13 maybe an LDPC coder having a length of 64800 and a code rate of 2/15. Acodeword having a length of 64800 may be divided into a total of 180 bitgroups. Each of the bit groups may include 360 bits, i.e., the parallelfactor of an LDPC codeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

In this case, the bit interleaver 14 prevents the performance of errorcorrection code from being degraded by effectively distributing bursterrors occurring in a channel. In this case, the bit interleaver 14 maybe separately designed in accordance with the length and code rate ofthe error correction code and the modulation order.

The interleaved codeword is modulated by a modulator 15, and is thentransmitted via an antenna 17.

In this case, the modulator 15 may be based on a concept includingsymbol mapper (symbol mapping device). In this case, the modulator 15may be a symbol mapping device performing 1024-symbol mapping which mapscodes onto 1024 constellations (symbols).

In this case, the modulator 15 may be a uniform modulator, such as aquadrature amplitude modulation (QAM) modulator, or a non-uniformmodulator.

The modulator 15 may be a symbol mapping device performing NUC(Non-Uniform Constellation) symbol mapping which uses 1024constellations (symbols).

The signal transmitted via the wireless channel 20 is received via theantenna 31 of the BICM reception device 30, and, in the BICM receptiondevice 30, is subjected to a process reverse to the process in the BICMdevice 10. That is, the received data is demodulated by a demodulator33, is deinterleaved by a bit deinterleaver 34, and is then decoded byan error correction decoder 35, thereby finally restoring theinformation bits.

It will be apparent to those skilled in the art that the above-describedtransmission and reception processes have been described within aminimum range required for a description of the features of the presentinvention and various processes required for data transmission may beadded.

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention.

Referring to FIG. 2, in the broadcast signal transmission and receptionmethod according to this embodiment of the present invention, input bits(information bits) are subjected to error-correction coding at stepS210.

That is, at step S210, an n-bit codeword is generated by encoding kinformation bits using the error-correction coder.

In this case, step S210 may be performed as in an LDPC encoding method,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,an interleaved codeword is generated by interleaving the n-bit codewordon a bit group basis at step S220.

In this case, the n-bit codeword may be an LDPC codeword having a lengthof 64800 and a code rate of 2/15. The codeword having a length of 64800may be divided into a total of 180 bit groups. Each of the bit groupsmay include 360 bits corresponding to the parallel factors of an LDPCcodeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,the encoded data is modulated at step S230.

That is, at step S230, the interleaved codeword is modulated using themodulator.

In this case, the modulator may be based on a concept including symbolmapper (symbol mapping device). In this case, the modulator may be asymbol mapping device performing 1024-symbol mapping which maps codesonto 1024 constellations (symbols).

In this case, the modulator may be a uniform modulator, such as a QAMmodulator, or a non-uniform modulator.

The modulator may be a symbol mapping device performing NUC (Non-UniformConstellation) symbol mapping which uses 1024 constellations (symbols).

Furthermore, in the broadcast signal transmission and reception method,the modulated data is transmitted at step S240.

That is, at step S240, the modulated codeword is transmitted over thewireless channel via the antenna.

Furthermore, in the broadcast signal transmission and reception method,the received data is demodulated at step S250.

That is, at step S250, the signal transmitted over the wireless channelis received via the antenna of the receiver, and the received data isdemodulated using the demodulator.

Furthermore, in the broadcast signal transmission and reception method,the demodulated data is deinterleaved at step S260. In this case, thedeinterleaving of step S260 may be reverse to the operation of stepS220.

Furthermore, in the broadcast signal transmission and reception method,the deinterleaved codeword is subjected to error correction decoding atstep S270.

That is, at step S270, the information bits are finally restored byperforming error correction decoding using the error correction decoderof the receiver.

In this case, step S270 corresponds to a process reverse to that of anLDPC encoding method, which will be described later.

An LDPC code is known as a code very close to the Shannon limit for anadditive white Gaussian noise (AWGN) channel, and has the advantages ofasymptotically excellent performance and parallelizable decodingcompared to a turbo code.

Generally, an LDPC code is defined by a low-density parity check matrix(PCM) that is randomly generated. However, a randomly generated LDPCcode requires a large amount of memory to store a PCM, and requires alot of time to access memory. In order to overcome these problems, aquasi-cyclic LDPC (QC-LDPC) code has been proposed. A QC-LDPC code thatis composed of a zero matrix or a circulant permutation matrix (CPM) isdefined by a PCM that is expressed by the following Equation 1:

$\begin{matrix}{{H = \begin{bmatrix}j^{a_{11}} & j^{a_{12}} & \ldots & j^{a_{1n}} \\j^{a_{21}} & j^{a_{22}} & \ldots & j^{a_{2n}} \\\vdots & \vdots & \ddots & \vdots \\J^{a_{m\; 1}} & J^{a_{m\; 2}} & \ldots & J^{a_{mn}}\end{bmatrix}},{{{for}\mspace{14mu} a_{ij}} \in \left\{ {0,1,\ldots \mspace{11mu},{L - 1},\infty} \right\}}} & (1)\end{matrix}$

In this equation, J is a CPM having a size of L×L, and is given as thefollowing Equation 2. In the following description, L may be 360.

$\begin{matrix}{J_{L \times L} = \begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \ldots & 0\end{bmatrix}} & (2)\end{matrix}$

Furthermore, J^(i) is obtained by shifting an L×L identity matrix I (J⁰)to the right i (0≤i<L) times, and J^(∞) is an L×L zero matrix.Accordingly, in the case of a QC-LDPC code, it is sufficient if onlyindex exponent i is stored in order to store J^(i), and thus the amountof memory required to store a PCM is considerably reduced.

FIG. 3 is a diagram illustrating the structure of a PCM corresponding toan LDPC code to according to an embodiment of the present invention.

Referring to FIG. 3, the sizes of matrices A and C are g×K and(N−K−g)×(K+g), respectively, and are composed of an L×L zero matrix anda CPM, respectively. Furthermore, matrix Z is a zero matrix having asize of g×(N−K−g), matrix D is an identity matrix having a size of(N−K−g)×(N−K−g), and matrix B is a dual diagonal matrix having a size ofg×g. In this case, the matrix B may be a matrix in which all elementsexcept elements along a diagonal line and neighboring elements below thediagonal line are 0, and may be defined as the following Equation 3:

$\begin{matrix}{B_{g \times g} = \begin{bmatrix}I_{L \times L} & 0 & 0 & \ldots & 0 & 0 & 0 \\I_{L \times L} & I_{L \times L} & 0 & \ldots & 0 & 0 & 0 \\0 & I_{L \times L} & I_{L \times L} & \vdots & 0 & 0 & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\0 & 0 & 0 & \ldots & I_{L \times L} & I_{L \times L} & 0 \\0 & 0 & 0 & \ldots & 0 & I_{L \times L} & I_{L \times L}\end{bmatrix}} & (3)\end{matrix}$

where I_(L×L) is an identity matrix having a size of L×L.

That is, the matrix B may be a bit-wise dual diagonal matrix, or may bea block-wise dual diagonal matrix having identity matrices as itsblocks, as indicated by Equation 3. The bit-wise dual diagonal matrix isdisclosed in detail in Korean Patent Application Publication No.2007-0058438, etc.

In particular, it will be apparent to those skilled in the art that whenthe matrix B is a bit-wise dual diagonal matrix, it is possible toperform conversion into a Quasi-cyclic form by applying row or columnpermutation to a PCM including the matrix B and having a structureillustrated in FIG. 3.

In this case, N is the length of a codeword, and K is the length ofinformation.

The present invention proposes a newly designed QC-LDPC code in whichthe code rate thereof is 2/15 and the length of a codeword is 64800, asillustrated in the following Table 1. That is, the present inventionproposes an LDPC code that is designed to receive information having alength of 8640 and generate an LDPC codeword having a length of 64800.

Table 1 illustrates the sizes of the matrices A, B, C, D and Z of theQC-LDPC code according to the present invention:

TABLE 1 Code Sizes rate Length A B C D Z 2/15 64800 1800 × 1800 × 54360× 54360 × 1800 × 8640 1800 10440 54360 54360

The newly designed LDPC code may be represented in the form of asequence (progression), an equivalent relationship is establishedbetween the sequence and matrix (parity bit check matrix), and thesequence may be represented, as follows:

Sequence Table 1st row: 615 898 1029 6129 8908 10620 13378 14359 2196423319 26427 26690 28128 33435 36080 40697 43525 44498 50994 2nd row: 1651081 1637 2913 8944 9639 11391 17341 22000 23580 32309 38495 41239 4407947395 47460 48282 51744 52782 3rd row: 426 1340 1493 2261 10903 1333614755 15244 20543 29822 35283 38846 45368 46642 46934 48242 49000 4920453370 4th row: 407 1059 1366 2004 5985 9217 9321 13576 19659 20808 3000931094 32445 39094 39357 40651 44358 48755 49732 5th row: 692 950 14442967 3929 6951 10157 10326 11547 13562 19634 34484 38236 42918 4468546172 49694 50535 55109 6th row: 1087 1458 1574 2335 3248 6965 1785623454 25182 37359 37718 37768 38061 38728 39437 40710 46298 50707 515727th row: 1098 1540 1711 7723 9549 9986 16369 19567 21185 21319 2575032222 32463 40342 41391 43869 48372 52149 54722 8th row: 514 1283 16356602 11333 11443 17690 21036 22936 24525 25425 27103 28733 29551 3920442525 49200 54899 54961 9th row: 357 609 1096 2954 4240 5397 8425 1397415252 20167 20362 21623 27190 42744 47819 49096 51995 55504 55719 10throw: 25 448 1501 11572 13478 24338 29198 29840 31428 33088 34724 3769837988 38297 40482 46953 47880 53751 54943 11st row: 328 1096 1262 1080212797 16053 18038 20433 20444 25422 32992 34344 38326 41435 46802 4876649807 52966 55751 12nd row: 34 790 987 5082 5788 10778 12824 18217 2327824737 28312 34464 36765 37999 39603 40797 43237 53089 55319 13rd row:226 1149 1470 3483 8949 9312 9773 13271 17804 20025 20323 30623 3857539887 40305 46986 47223 49998 52111 14th row: 1088 1091 1757 2682 55265716 9665 10733 12997 14440 24665 27990 30203 33173 37423 38934 4049445418 48393 15th row: 809 1278 1580 3486 4529 6117 6212 6823 7861 924411559 20736 30333 32450 35528 42968 44485 47149 54913 16th row: 369 5251622 2261 6454 10483 11259 16461 17031 20221 22710 25137 26622 2790430884 31858 44121 50690 56000 17th row: 423 1291 1352 7883 26107 2615726876 27071 31515 35340 35953 36608 37795 37842 38527 41720 46206 4799853019 18th row: 540 662 1433 2828 14410 22880 24263 24802 28242 2839635928 37214 39748 43915 44905 46590 48684 48890 55926 19th row: 214 12911622 7311 8985 20952 22752 23261 24896 25057 28826 37074 37707 3874246026 51116 51521 52956 54213 20th row: 109 1305 1676 2594 7447 894314806 16462 19730 23430 24542 34300 36432 37133 41199 43942 45860 4759848401 49407 21st row: 242 388 1360 6721 14220 21029 22536 25126 3225133182 39192 42436 44144 45252 46238 47369 47607 47695 50635 51469 22ndrow: 199 958 1111 13661 18809 19234 21459 25221 25837 28256 36919 3903139107 39262 43572 45018 45959 48006 52387 55811 23rd row: 668 1087 14512945 3319 12519 21248 21344 22627 22701 28152 29670 31430 32655 3853342233 43200 44013 44459 51398 24th row: 244 1133 1665 8222 8740 1128512774 15922 20147 20978 28927 35086 40197 40583 41066 41223 42104 4465045391 48437 25th row: 5623 8050 9679 12978 15846 16049 21807 23364 2722627758 28661 38147 46337 48141 51364 51927 55124 26th row: 10369 1370414491 18632 19430 21218 33392 36182 36722 37342 37415 46322 47449 5113653392 54356 55108 27th row: 7460 9411 11132 11739 13722 15501 2558826463 26738 31980 31981 35002 39659 39783 41581 51358 55114 28th row:8915 15253 15264 16513 16896 18367 19110 23492 32074 33302 42443 4379744715 47538 48515 53464 53548 29th row: 5884 8910 10123 11311 1365414207 16122 18113 23100 23784 24825 39629 46372 52454 52799 55039 55973

An LDPC code that is represented in the form of a sequence is beingwidely used in the DVB standard.

According to an embodiment of the present invention, an LDPC codepresented in the form of a sequence is encoded, as follows. It isassumed that there is an information block S=(s₀, s₁, . . . , s_(K−1))having an information size K. The LDPC encoder generates a codewordΛ=(λ₀, λ₁, λ₂, . . . , λ_(N−1)) having a size of N=K+M₁+M₂ using theinformation block S having a size K. In this case, M₁=g, and M₂=N−K−g.Furthermore, M₁ is the size of parity bits corresponding to the dualdiagonal matrix B, and M₂ is the size of parity bits corresponding tothe identity matrix D. The encoding process is performed, as follows:

Initialization:

λ_(i) =s _(i) for i=0,1, . . . ,K−1

p _(j)=0 for j=0,1, . . . ,M ₁ +M ₂−1  (4)

First information bit λ₀ is accumulated at parity bit addressesspecified in the 1st row of the sequence of the Sequence Table. Forexample, in an LDPC code having a length of 64800 and a code rate of2/15, an accumulation process is as follows:

p₆₁₅ = p₆₁₅ ⊕ λ₀ p₈₉₈ = p₈₉₈ ⊕ λ₀ p₁₀₂₉ = p₁₀₂₉ ⊕ λ₀ p₆₁₂₉ = p₆₁₂₉ ⊕ λ₀p₈₉₀₈ = p₈₉₀₈ ⊕ λ₀ p₁₀₆₂₀ = p₁₀₆₂₀ ⊕ λ₀ p₁₃₃₇₈ = p₁₃₃₇₈ ⊕ λ₀ p₁₄₃₅₉ =p₁₄₃₅₉ ⊕ λ₀ p₂₁₉₆₄ = p₂₁₉₆₄ ⊕ λ₀ p₂₃₃₁₉ = p₂₃₃₁₉ ⊕ λ₀ p₂₆₄₂₇ = p₂₆₄₂₇ ⊕λ₀ p₂₆₆₉₀ = p₂₆₆₉₀ ⊕ λ₀ p₂₈₁₂₈ = p₂₈₁₂₈ ⊕ λ₀ p₃₃₄₃₅ = p₃₃₄₃₅ ⊕ λ₀ p₃₆₀₈₀= p₃₆₀₈₀ ⊕ λ₀ p₄₀₆₉₇ = p₄₀₆₉₇ ⊕ λ₀ p₄₃₅₂₅ = p₄₃₅₂₅ ⊕ λ₀ p₄₄₄₉₈ = p₄₄₄₉₈⊕ λ₀ p₅₀₉₉₄ = p₅₀₉₉₄ ⊕ λ₀where the addition ⊕ occurs in GF(2).

The subsequent L−1 information bits, that is, λ_(m)=1, 2, . . . , L−1,are accumulated at parity bit addresses that are calculated by thefollowing Equation 5:

(x+m×

₁) mod M ₁ if x<M ₁

M ₁+{(x−M ₁ +m×

₂) mod M ₂} if x≥M ₁  (5)

where x denotes the addresses of parity bits corresponding to the firstinformation bit λ₀, that is, the addresses of the parity bits specifiedin the first row of the sequence of the Sequence Table,

₁=M₁/L,

₂=M₂/L, and L=360. Furthermore,

₁ and

₂ are defined in the following Table 2. For example, for an LDPC codehaving a length of 64800 and a code rate of 2/15, M₁=1800,

₁=5, M₂=54360,

₂=151 and L=360, and the following operations are performed on thesecond bit λ₁ using Equation 5:

p₆₂₀ = p₆₂₀ ⊕ λ₁ p₉₀₃ = p₉₀₃ ⊕ λ₁ p₁₀₃₄ = p₁₀₃₄ ⊕ λ₁ p₆₂₈₀ = p₆₂₈₀ ⊕ λ₁p₉₀₅₉ = p₉₀₅₉ ⊕ λ₁ p₁₀₇₇₁ = p₁₀₇₇₁ ⊕ λ₁ p₁₃₅₂₉ = p₁₃₅₂₉ ⊕ λ₁ p₁₄₅₁₀ =p₁₄₅₁₀ ⊕ λ₁ p₂₂₁₁₅ = p₂₂₁₁₅ ⊕ λ₁ p₂₃₄₇₀ = p₂₃₄₇₀ ⊕ λ₁ p₂₆₅₇₈ = p₂₆₅₇₇₈ ⊕λ₁ p₂₆₈₄₁ = p₂₆₈₄₁ ⊕ λ₁ p₂₈₂₇₉ = p₂₈₂₇₉ ⊕ λ₁ p₃₃₅₈₆ = p₃₃₅₈₆ ⊕ λ₁ p₃₆₂₃₁= p₃₆₂₃₁ ⊕ λ₁ p₄₀₈₄₈ = p₄₀₈₄₈ ⊕ λ₁ p₄₃₆₇₆ = p₄₃₆₇₆ ⊕ λ₁ p₄₄₆₄₉ = p₄₄₆₄₉⊕ λ₁ p₅₁₁₄₅ = p₅₁₁₄₅ ⊕ λ₁

Table 2 illustrates the sizes of M₁,

₁, M₂ and

₂ of the designed QC-LDPC code:

TABLE 2 Sizes Code rate Length M₁ M₂

 ₁

 ₂ 2/15 64800 1800 54360 5 151

The addresses of parity bit accumulators for new 360 information bitsfrom λ_(L) to λ_(2L-1) are calculated and accumulated from Equation 5using the second row of the sequence.

In a similar manner, for all groups composed of new L information bits,the addresses of parity bit accumulators are calculated and accumulatedfrom Equation 5 using new rows of the sequence.

After all the information bits from λ₀ to λ_(K−1) have been exhausted,the operations of the following Equation 6 are sequentially performedfrom i=1:

p _(i) =p _(i) ⊕p _(i-1) for i=0,1, . . . ,M ₁−1  (6)

Thereafter, when a parity interleaving operation, such as that of thefollowing Equation 7, is performed, parity bits corresponding to thedual diagonal matrix B are generated:

λ_(K+L·t+s)=

for 0≤s<L, 0≤t<

₁  (7)

When the parity bits corresponding to the dual diagonal matrix B havebeen generated using K information bits λ₀, λ₁, . . . , λ_(K−1), paritybits corresponding to the identity matrix D are generated using the M₁generated parity bits λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹.

For all groups composed of L information bits from λ_(K) to λ_(K+M) ₁⁻¹, the addresses of parity bit accumulators are calculated using thenew rows (starting with a row immediately subsequent to the last rowused when the parity bits corresponding to the dual diagonal matrix Bhave been generated) of the sequence and Equation 5, and relatedoperations are performed.

When a parity interleaving operation, such as that of the followingEquation 8, is performed after all the information bits from Δ_(K) toλ_(K+M) ₁ ⁻¹ have been exhausted, parity bits corresponding to theidentity matrix D are generated:

λ_(K+M) ₁ _(+L·t+s)=

for 0≤s<L, 0≤t<

₂  (8)

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800.

Referring to FIG. 4, it can be seen that an LDPC codeword having alength of 64800 is divided into 180 bit groups (a 0th group to a 179thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 64800is divided into 180 bit groups, as illustrated in FIG. 4, and each ofthe bit groups includes 360 bits.

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200.

Referring to FIG. 5, it can be seen that an LDPC codeword having alength of 16200 is divided into 45 bit groups (a 0th group to a 44thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 16200is divided into 45 bit groups, as illustrated in FIG. 5, and each of thebit groups includes 360 bits.

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence.

Referring to FIG. 6, it can be seen that interleaving is performed bychanging the order of bit groups by a designed interleaving sequence.

For example, it is assumed that an interleaving sequence for an LDPCcodeword having a length of 16200 is as follows:

interleaving sequence={24 34 15 11 2 28 17 25 5 38 19 13 6 39 1 14 33 3729 12 42 31 30 32 36 40 26 35 44 4 16 8 20 43 21 7 0 18 23 3 10 41 9 2722}

Then, the order of the bit groups of the LDPC codeword illustrated inFIG. 4 is changed into that illustrated in FIG. 6 by the interleavingsequence.

That is, it can be seen that each of the LDPC codeword 610 and theinterleaved codeword 620 includes 45 bit groups, and it can be also seenthat, by the interleaving sequence, the 24th bit group of the LDPCcodeword 610 is changed into the 0th bit group of the interleaved LDPCcodeword 620, the 34th bit group of the LDPC codeword 610 is changedinto the 1st bit group of the interleaved LDPC codeword 620, the 15thbit group of the LDPC codeword 610 is changed into the 2nd bit group ofthe interleaved LDPC codeword 620, and the 11st bit group of the LDPCcodeword 610 is changed into the 3rd bit group of the interleaved LDPCcodeword 620, and the 2nd bit group of the LDPC codeword 610 is changedinto the 4th bit group of the interleaved LDPC codeword 620.

An LDPC codeword (u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹) having a length ofN_(ldpc) is divided into N_(group)=N_(ldpc)/360 bit groups, as inEquation 9 below:

X _(j) ={u _(k)|360×j≤k<360×(j+1), 0≤k<N _(ldpc)} for 0≤j<N_(group)  (9)

where X_(j) is an j-th bit group, and each X_(j) is composed of 360bits.

The LDPC codeword divided into the bit groups is interleaved, as inEquation 10 below:

Y _(j) =X _(π(j)) 0≤j≤N _(group)  (10)

where Y_(j) is an interleaved j-th bit group, and π(j) is a permutationorder for bit group-based interleaving (bit group-unit interleaving).The permutation order corresponds to the interleaving sequence ofEquation 11 below:

interleaving sequence={157 25 107 160 37 138 111 35 29 44 15 162 66 2049 126 89 147 159 174 142 26 146 10 164 152 57 110 83 167 169 16 6 17262 173 7 145 4 67 115 50 39 72 79 74 40 132 42 30 163 161 55 143 63 11786 121 2 28 69 150 24 177 43 158 27 21 128 46 118 114 127 135 92 76 1994 179 3 52 101 137 84 73 108 91 120 47 1 102 58 68 82 59 119 64 31 61105 103 151 124 70 8 155 90 166 41 45 178 113 140 75 148 109 100 125 11116 34 36 176 170 156 136 171 122 78 87 106 123 149 17 99 175 18 9 165153 12 81 77 60 93 104 13 5 88 96 141 133 154 144 48 97 23 14 98 53 134112 65 0 130 32 168 33 131 22 38 56 80 95 71 85 139 129 51 54}  (11)

That is, when each of the codeword and the interleaved codeword includes180 bit groups ranging from a 0th bit group to a 179th bit group, theinterleaving sequence of Equation 11 means that the 157th bit group ofthe codeword becomes the 0th bit group of the interleaved codeword, the25th bit group of the codeword becomes the 1st bit group of theinterleaved codeword, the 107th bit group of the codeword becomes the2nd bit group of the interleaved codeword, the 160th bit group of thecodeword becomes the 3rd bit group of the interleaved codeword, . . . ,the 51nd bit group of the codeword becomes the 178th bit group of theinterleaved codeword, and the 54th bit group of the codeword becomes the179th bit group of the interleaved codeword.

In particular, the interleaving sequence of Equation 11 has beenoptimized for a case where 1024-symbol mapping (NUC symbol mapping) isemployed and an LDPC coder having a length of 64800 and a code rate of2/15 is used.

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention.

Referring to FIG. 7, the bit interleaver according to the presentembodiment includes memories 710 and 730 and a processor 720.

The memory 710 stores an LDPC codeword having a length of 64800 and acode rate of 2/15.

The processor 720 generates an interleaved codeword by interleaving theLDPC codeword on a bit group basis corresponding to the parallel factorof the LDPC codeword.

In this case, the parallel factor may be 360. In this case, each of thebit groups may include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

The memory 730 provides the interleaved codeword to a modulator for1024-symbol mapping.

In this case, the modulator may be a symbol mapping device performingNUC (Non-Uniform Constellation) symbol mapping.

The memories 710 and 730 may correspond to various types of hardware forstoring a set of bits, and may correspond to a data structure, such asan array, a list, a stack, a queue or the like.

In this case, the memories 710 and 730 may not be physically separatedevices, but may correspond to different addresses of a physicallysingle device. That is, the memories 710 and 730 are not physicallydistinguished from each other, but are merely logically distinguishedfrom each other.

The error-correction coder 13 illustrated in FIG. 1 may be implementedin the same structure as in FIG. 7.

That is, the error-correction coder may include memories and aprocessor. In this case, the first memory is a memory that stores anLDPC codeword having a length of 64800 and a code rate of 2/15, and asecond memory is a memory that is initialized to 0.

The memories may correspond to λ_(i)(i=0, 1, . . . , N−1) and P_(j)(j=0,1, . . . , M₁+M₂−1), respectively.

The processor may generate an LDPC codeword corresponding to informationbits by performing accumulation with respect to the memory using asequence corresponding to a parity check matrix (PCM).

In this case, the accumulation may be performed at parity bit addressesthat are updated using the sequence of the above Sequence Table.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits and having a lengthof 8640 (=K), a first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹corresponding to a dual diagonal matrix included in the PCM and having alength of 1800 (=M₁=g), and a second parity part λ_(K+M) ₁ , λ_(K+M) ₁₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM and having a length of 54360 (=M₂).

In this case, the sequence may have a number of rows equal to the sum(8640/360+1800/360=29) of a value obtained by dividing the length of thesystematic part, i.e., 8640, by a CPM size L corresponding to the PCM,i.e., 360, and a value obtained by dividing the length M₁ of the firstparity part, i.e., 1800, by 360.

As described above, the sequence may be represented by the aboveSequence Table.

In this case, the second memory may have a size corresponding to the sumM₁+M₂ of the length M₁ of the first parity part and the length M₂ of thesecond parity part.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addresses,specified in respective rows of the sequence, with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM,

₁ may be M₁/L, M₁ may be the size of the first parity part,

₂ may be M₂/L, and M₂ may be the size of the second parity part.

In this case, it may be possible to perform the accumulation whilerepeatedly changing the rows of the sequence by the CPM size L (=360) ofthe PCM, as described above.

In this case, the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹may be generated by performing parity interleaving using the firstmemory and the second memory, as described in conjunction with Equation7.

In this case, the second parity part λ_(K+M) ₁ , λ_(K+M) ₁ ₊₁, . . . ,λ_(K+M) ₁ _(+M) ₂ ⁻¹ may be generated by performing parity interleavingusing the first memory and the second memory after generating the firstparity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ and then performing theaccumulation using the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M)₁ ⁻¹ and the sequence, as described in conjunction with Equation 8.

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

Referring to FIG. 8, in the bit interleaving method according to thepresent embodiment, an LDPC codeword having a length of 64800 and a coderate of 2/15 is stored at step S810.

In this case, the LDPC codeword may be represented by (u₀, u₁, . . . ,u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and may be divided into 180bit groups each composed of 360 bits, as in Equation 9.

Furthermore, in the bit interleaving method according to the presentembodiment, an interleaved codeword is generated by interleaving theLDPC codeword on a bit group basis at step S820.

In this case, the size of the bit group may correspond to the parallelfactor of the LDPC codeword.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

In this case, the parallel factor may be 360, and each of the bit groupsmay include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

Moreover, in the bit interleaving method according to the presentembodiment, the interleaved codeword is output to a modulator for1024-symbol mapping at step 830.

In accordance with at least one embodiment of the present invention,there is provided an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

In accordance with at least one embodiment of the present invention,there is provided a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 2/15 and a modulatorperforming 1024-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

Although the specific embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible without departing from the scope and spirit of the invention asdisclosed in the accompanying claims.

What is claimed is:
 1. A method of transmitting a broadcast signal,comprising: storing a low-density parity check (LDPC) codeword having alength of 64800 and a code rate of 2/15; generating an interleavedcodeword by interleaving the LDPC codeword on a bit group basis, thesize of the bit group corresponding to a parallel factor of the LDPCcodeword; storing the interleaved codeword corresponding to 1024-symbolmapping, performing 1024-symbol mapping for generating a broadcastsignal; and transmitting the broadcast signal over a physical channel,wherein the interleaving is performed using the following equation usingpermutation order:Y _(j) =X _(π(j)) 0≤j<N _(group) where X_(π(j)) is the π(j)th bit group,Y_(j) is an interleaved j-th bit group, and π(j) is a permutation orderfor bit group-based interleaving, wherein the permutation ordercorresponds to an interleaving sequence represented by the followinginterleaving sequence={157 25 107 160 37 138 111 35 29 44 15 162 66 2049 126 89 147 159 174 142 26 146 10 164 152 57 110 83 167 169 16 6 17262 173 7 145 4 67 115 50 39 72 79 74 40 132 42 30 163 161 55 143 63 11786 121 2 28 69 150 24 177 43 158 27 21 128 46 118 114 127 135 92 76 1994 179 3 52 101 137 84 73 108 91 120 47 1 102 58 68 82 59 119 64 31 61105 103 151 124 70 8 155 90 166 41 45 178 113 140 75 148 109 100 125 11116 34 36 176 170 156 136 171 122 78 87 106 123 149 17 99 175 18 9 165153 12 81 77 60 93 104 13 5 88 96 141 133 154 144 48 97 23 14 98 53 134112 65 0 130 32 168 33 131 22 38 56 80 95 71 85 139 129 51 54}, whereinthe interleaved codeword is interleaved by the interleaving sequence onthe bit group basis before performing the 1024-symbol mapping so as todistribute burst errors occurring in the transmission signal transmittedover the wireless channel.
 2. The method of claim 1, wherein the1024-symbol mapping is a Non-Uniform Constellation (NUC) symbol mappingwhich corresponds to 1024 constellations.
 3. The method of claim 2,wherein the parallel factor is 360, and the bit group includes 360 bits.4. The method of claim 3, wherein the LDPC codeword is represented by(u₀, u₁, . . . , u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and isdivided into 45 bit groups each including 360 bits, as in the followingequation:X _(j) ={u _(k)|360×j≤k<360×(j+1), 0≤k<N _(ldpc)} for 0≤j<N _(group)where X_(j) is an j-th bit group, N_(ldpc) is 64800, and N_(group) is180.